Inverse modelling for mercury over Europe

Texte intégral

(1)Inverse modelling for mercury over Europe Y. Roustan, Marc Bocquet. To cite this version: Y. Roustan, Marc Bocquet. Inverse modelling for mercury over Europe. Atmospheric Chemistry and Physics Discussions, European Geosciences Union, 2006, 6 (1), pp.795-838. �hal-00327809�. HAL Id: hal-00327809 https://hal.archives-ouvertes.fr/hal-00327809 Submitted on 30 Jan 2006. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés..

(2) Atmos. Chem. Phys. Discuss., 6, 795–838, 2006 www.atmos-chem-phys.org/acpd/6/795/ SRef-ID: 1680-7375/acpd/2006-6-795 European Geosciences Union. Atmospheric Chemistry and Physics Discussions. ACPD 6, 795–838, 2006. Inverse modelling for mercury over Europe Y. Roustan and M. Bocquet. Inverse modelling for mercury over Europe. Title Page Abstract. Introduction. Conclusions. References. Tables. Figures. J. I. J. I. Back. Close. Y. Roustan and M. Bocquet ´ Centre d’Enseignement et de Recherche en Environnement Atmospherique, Joint laboratory ´ ´ Ecole Nationale des Ponts et Chaussees/EDF R&D, avenue Blaise Pascal, 77 455 Champs sur Marne, France Received: 12 October 2005 – Accepted: 21 November 2005 – Published: 30 January 2006 Correspondence to: Y. Roustan (roustan@cerea.enpc.fr) © 2006 Author(s). This work is licensed under a Creative Commons License.. Full Screen / Esc. Print Version Interactive Discussion. EGU 795.

(3) Abstract. 5. 10. 15. ACPD. The fate and transport of mercury over Europe is studied using a regional Eulerian transport model. Because gaseous elemental mercury is a long-lived species in the atmosphere, boundary conditions must be properly taken into account. Ground measurements of gaseous mercury are very sensitive to the uncertainties attached to those forcing conditions. Inverse modelling can help to constrain the forcing fields and help to improve the predicted mercury concentrations. More generally, it allows to reduce the weaknesses of a regional model against a global or hemispherical model for such diffuse trace constituent. Adjoint techniques are employed to relate rigorously and explicitly the measurements to the forcing fields. This way, the inverse problem is clearly defined. Using EMEP measurements of gaseous mercury and performing the inversions, it is shown that boundary conditions can be improved significantly as well as the forecast concentrations. Using inverse modelling to improve the emission inventory is however much more difficult since there are currently not enough mercury monitoring stations, and their location far from Europe centre. 1. Introduction. 20. 25. Gaseous elemental mercury (GEM) makes up more than 95% of the mass of atmospheric mercury (Ryaboshapko et al., 2002), but mercury can also be found under oxidised forms, both in gaseous and aqueous phases and possibly linked to the particulate matter. Life times of mercury species strongly vary from one year for GEM (Lindqvist and Rodhe, 1985), days to weeks for mercury adsorbed/absorbed to particulate matter, and hours to days for oxidised gaseous species (Seigneur et al., 2003). These life times are obviously driven by the rates of dry and wet deposition which are in turn governed by physical and chemical properties of the species. Owing to its long life time, mercury is considered as a global pollutant. Hence the Chemistry Transport Models (CTM) currently used to simulate atmospheric mercury 796. 6, 795–838, 2006. Inverse modelling for mercury over Europe Y. Roustan and M. Bocquet. Title Page Abstract. Introduction. Conclusions. References. Tables. Figures. J. I. J. I. Back. Close. Full Screen / Esc. Print Version Interactive Discussion. EGU.

(4) 5. 10. 15. 20. 25. fate and transport run on a global domain (Seigneur et al., 2001) or a hemispherical one (Ilyin et al., 2002; Christensen et al., 2004). Such models proved well suited to the study of transboundary pollution. Nevertheless regional models remain suitable for impact studies needing finer spatial resolution whereas global model may have too coarse resolution to get accurate estimations of local deposition fluxes. Some simulations are still performed within a restricted domain (Lin and Tao, 2003; Bullock and Brehme, 2002), and generally stand as a first step in atmospheric mercury model development. Consequently to its long life time GEM is rather homogeneously mixed in the atmosphere. Typical concentrations are in the range of one to two ng m−3 . With modelling issues in mind, this behaviour suggests that boundary conditions for a limited area model are crucial. As a consequence a regional model can account for mercury dispersion only if boundary conditions are properly addressed. This may be achieved though inverse modelling. Because of the linearity of dispersion and all physical processes of mercury (dry deposition, wet scavenging, chemistry), the forecasted concentrations can be related explicitly to the forcing fields (in particular boundary conditions). In the case of atmospheric mercury, this has been recently carried out using adjoint 1 techniques (Roustan and Bocquet ). In Sect. 2 of this paper, the mercury dispersion model used is detailed. A few results about the global budget of mercury in a regional domain is given, in order to emphasise the role of mercury exchanges in and out of the domain. In Sect. 3, the way adjoint methods should be used to establish the inverse problem is advocated, both for the continuous and the numerical (discrete) models. In Sect. 4, an inverse modelling approach building on the tools introduced previously and which aims mainly at improving boundary conditions is tested. In Sect. 5, the inverse modelling methodology is generalised and tested with a complex chemistry scheme, accounting for oxidised mercury species. Conclusions are given in Sect. 6.. ACPD 6, 795–838, 2006. Inverse modelling for mercury over Europe Y. Roustan and M. Bocquet. Title Page Abstract. Introduction. Conclusions. References. Tables. Figures. J. I. J. I. Back. Close. Full Screen / Esc. Print Version Interactive Discussion. 1. Roustan, Y. and Bocquet, M.: Sensitivity analysis for mercury over Europe, J. Geophys. Res., submitted, 2005.. 797. EGU.

(5) 2. Simulating mercury over Europe. ACPD. The following equation describes the transport and fate of mercury concentration, c, under the influence of well identified atmospheric processes: ∂c + div (uc) − div (K∇c) + Λ c = σ ∂t 5. 10. (1). The temporal evolution of mercury concentration is governed by, from left to right in Eq. (1), the advection by the wind field u, the turbulent diffusion (characterised by the eddy diffusion tensor K), the wet scavenging including a parameterisation of the chemistry (space and time varying coefficient Λ) and finally sources (σ). Dry deposition (with vd the dry deposition velocity) and surface emission (E ) are enforced as a ground boundary condition (the normal surface vector, n, is outward oriented): (K∇c) · n = vd c − E .. (2). 2.1. Physical and chemical parameterisations. 15. 20. The chemistry model which will be used has been proposed in Petersen et al. (1995). In this model elemental mercury is considered as a passive tracer in gaseous phase but as a reactive chemical in the aqueous phase. Ozone is the only oxidant species accounting for the oxidised mercury formation. Oxidised mercury in aqueous phase can form a complex with sulfite ions or it can be adsorbed by particulate matter. The complex may either be decomposed and give elemental mercury or it may be adsorbed by particulate matter in turn (see Fig. 1). More reactions and species are represented in currently developed models (Ryaboshapko et al., 2002). The aim is to get better evaluation of oxidised species concentration in order to improve deposition flux patterns. Yet, this work will mostly require a correct modelling of the GEM concentration field. Forced concentration fields are used 798. 6, 795–838, 2006. Inverse modelling for mercury over Europe Y. Roustan and M. Bocquet. Title Page Abstract. Introduction. Conclusions. References. Tables. Figures. J. I. J. I. Back. Close. Full Screen / Esc. Print Version Interactive Discussion. EGU.

(6) 5. 10. 15. 20. for ozone and soot particles. As mentioned previously, this model is based on several equilibria hypotheses, which allows to represent chemistry through a scavenging ratio. An interesting point is that the chemistry-scavenging term in Eq. (1) is linear (so are the advection and diffusion terms). In practice, numerically modelled GEM nearly behaves like a passive tracer. Wet scavenging represent pollutant mass transfer from the atmosphere to the soil during precipitation events. The mass could be collected by cloud drops (in cloud scavenging) or rain drops (below-cloud scavenging). GEM is also removed from the atmosphere by dry deposition. Often dry deposition is decomposed into three consecutive processes that bring pollutant from atmosphere to soil surface under dry conditions (Wesely and Hicks, 2000). The first one is the turbulent diffusion that is the dominant process in most of the layer between the height where dry deposition velocity is estimated and the soil. In the quasi-laminar layer gaseous molecular diffusion becomes the major process. The mass transfer processes from the air to the canopy completes the removal mechanism. A common big-leaf deposition resistance model is used to compute dry deposition velocities. Resistances parameterisation are inspired by Baer and Nester (1992) with some improvements, in particular for the quasi-laminar boundary resistance over sea (Hicks and Liss, 1976) and the canopy water content consideration in canopy resistance (Brook et al., 1999). Those parameterisations are further detailed in Roustan et al. (2005). 2.2. A regional domain model. 25. The transport and physics of mercury is meant here to be simulated over Europe. The ◦ ◦ domain which is considered (Fig. 2) extends in space from 12.375 W to 37.125 E ◦ ◦ in longitude and from 36 N to 72 N in latitude (Europe). Direct and backward (adjoint modelling) simulations are performed for the year 2001. A constant space step ◦ of 1.125 is taken along longitude and latitude for the horizontal grid of 44×32 cells, respectively. The 14 vertical levels cover atmosphere from the ground to 5233 m in 799. ACPD 6, 795–838, 2006. Inverse modelling for mercury over Europe Y. Roustan and M. Bocquet. Title Page Abstract. Introduction. Conclusions. References. Tables. Figures. J. I. J. I. Back. Close. Full Screen / Esc. Print Version Interactive Discussion. EGU.

(7) 5. 10. 15. 20. relative height. The domain is designated by Ω and it is the product of its spatial and temporal components Ω=D×[0, τ]. The boundaries of the domain Ω are denoted ∂Ω0 , ∂Ωτ , ∂Ωb , ∂Ωt , ∂Ωn , ∂Ωs , ∂Ωw and ∂Ωe , for respectively the initial, final, surface, top, North, South, West and East boundaries. The boundary of the space domain is denoted ∂D. A distinction is to be made between border interfaces where the wind is incoming, and border interfaces where it is outgoing. Hence the spatial boundary splits into ∂D=∂D+ ∪ ∂D− (+ means incoming, and − meansS outgoing). Note that this decomposition is time-dependent. We will also note ∂Ω± = t ∂D± [t]. Finally, ∂D, the spatial boundary of D, is made up of the bottom (surface), top, North, South, West and East borders, ∂Db , ∂Dt , ∂Dn , ∂Ds , Dw , and ∂De , respectively. It is a rather limited horizontal area in comparison to what is currently done to study mercury impact over Europe (Ilyin et al., 2003). Because of its long atmospheric life time GEM is considered to be a global pollutant, hence should be studied by means of a global model. Since the magnitude order of GEM residence time and inter-hemispheric exchange time are quite similar hemispheric model may be relevant. However such models need much more data and computing time to perform simulation with relatively coarse spatial resolution. One aim of this work is to evaluate the feasibility and the interest of inverse modelling on boundary conditions to avoid use of global and hemispheric models. 2.3. Mercury mass budget over Europe. 25. A mass budget is a diagnosis tool to test the accuracy of the numerical transport model. It helps ensuring that numerics are under control. In addition it provides with data on the magnitude of transboundary mercury fluxes, as well as ground emissions and sources. It is a first albeit gross view on the potential drawbacks of a limited area model versus a global or hemispherical model. A simulation has been performed for the year 2001, using the CTM P OLAIR 3D, whose characteristics will further be detailed in Sect. 3.2. The emission data (see 800. ACPD 6, 795–838, 2006. Inverse modelling for mercury over Europe Y. Roustan and M. Bocquet. Title Page Abstract. Introduction. Conclusions. References. Tables. Figures. J. I. J. I. Back. Close. Full Screen / Esc. Print Version Interactive Discussion. EGU.

(8) 5. 10. 15. 20. 25. Fig. 2) are those provided by the Meteorological Synthesising Centre – East (MSCE) for the year 2001, which is one of the European Monitoring and Evaluation Program (EMEP) centre (http://www.msceast.org/). Mercury emissions are usually classified into three types, anthropogenic, natural and reemission (Ryaboshapko et al., 1998). For the simulation anthropogenic emissions are split into ground emission and sources (emissions in the bulk) at the second vertical level. Meteorological fields are derived from re-analysis of the European Centre for Medium-Range Weather Forecasts (ECMWF) with a six hours frequency. Vertical wind fields are diagnosed in order to ensure mass conservation under the incompressible atmosphere hypothesis. A homogeneous initial concentration of 1.5 ng.m−3 is taken in the bulk. The simulation time step is 900 s, data are linearly interpolated between each data time step. The following uniform boundary conditions are implemented: 1.75 ng.m−3 at West, 1.7 ng.m−3 at East, 1.5 ng.m−3 at South and 1.42 ng.m−3 at North. These values are proposed by the MSC-E in a first approach. In addition a value of 1.6 ng.m−3 at the top of the domain was chosen. For each boundary of the domain total mass fluxes have been computed. For each type of emission, the total released mass is given. The initial and final mercury masses present in the domain are also part of the budget. Those fluxes are listed in Table 1. At first this budget confirms the consequent contribution of boundary fluxes to the GEM concentration in the bulk, especially on the western border, which is consistent with the average atmospheric circulation over Europe from West to North-East. Secondly the initial and final masses are similar and relatively low in comparison to advected fluxes. In this respect, Fig. 3 unveils that the initial conditions are almost forgotten after a two weeks spin-up time. Therefore the final mass is probably mainly ascribable to meteorological, boundary conditions and dynamical input of mercury. The absolute values of fluxes seem far superior to the mass injected by emissions. Having in mind to extract information from such a regional model about (for instance) the impact of emissions in Europe, this last remark may sound compromising. How801. ACPD 6, 795–838, 2006. Inverse modelling for mercury over Europe Y. Roustan and M. Bocquet. Title Page Abstract. Introduction. Conclusions. References. Tables. Figures. J. I. J. I. Back. Close. Full Screen / Esc. Print Version Interactive Discussion. EGU.

(9) 5. 10. ever those figures do not give direct information about the sensitivity of mercury concentrations near the ground. Contributions of surface emissions and sources appear moderate. However since the spatial origin of these fluxes is close to the ground one can expect to find a relatively high sensitivity to surface concentrations. The fluxes at the top of the domain are also important. However the exchange surface is much more extended than those of the other domain boundaries. Since mass exchanges between the top, belonging to the free troposphere, and the surface, in the atmospheric boundary layer, are rather limited, it seems rational to assume there is little consequence on surface concentrations. The weakness of the chemistry mechanism which largely underestimates the wet deposition flux is also shown, but in a first approach this is not a worrying point for now. The budget is theoretically balanced. This has been checked numerically, with a very moderate unbalance of 0.1 t of elemental mercury. 3. Adjoint transport in an open domain. 15. As for any inverse problems, we need to establish the link between the output (the measurements) and the forcing fields. This can be carried out rigorously with adjoint analytical and numerical techniques. 3.1. Continuous analysis. ACPD 6, 795–838, 2006. Inverse modelling for mercury over Europe Y. Roustan and M. Bocquet. Title Page Abstract. Introduction. Conclusions. References. Tables. Figures. J. I. J. I. Back. Close. 1. 20. Details of the calculation can be found in Roustan and Bocquet (2005) , as well as references to the use of adjoint techniques in air quality models. Here we merely give the definitions and results. A concentration measurement (of value Rµi , performed on site i ) is characterised by a sampling function πi : Ω → R, such that Ω dtdx πi (x, t)=1 and Z µi = dtdx πi (x, t) c(x, t) . (3) Ω. 802. Full Screen / Esc. Print Version Interactive Discussion. EGU.

(10) ∗. Let ci be a solution of the retro-transport equation, forced by πi : −. 5. 10. ∂c∗i ∂t. − div uc∗i − div K∇c∗i + Λc∗i = πi .. 20. (4). The justification for introducing c∗i will appear thereafter. To characterise c∗i completely, boundary and initial conditions must be specified. As is clearly seen from Eq. (4), the adjoint solution c∗i corresponds to a transport backward in time. The wind field is the opposite of the direct model wind field. As a consequence, an outgoing (from the domain D) wind flow for the direct model is actually an incoming wind flow for the adjoint model. In order to specify the advective incoming mercury, we therefore need to specify its concentration on ∂D− at any time. For simplicity, ∀ (x, t) ∈ ∂Ω− ,. 15. ACPD. c∗i (x, t) = 0 ,. (5). is assumed (among other possible consistent choices). ∗ In addition, the diffusive fluxes −K∇c and −K∇ci at the boundary ∂D are supposed both negligible when compared to the advected flux, or imposed (when possible) as 0. However at the surface, −K∇c is no different than the surface emission J. In a similar fashion, −K∇c∗i could be chosen at the surface, a given value J ∗i which is to be prescribed later on. Finally, the adjoint concentration field c∗i is set to be null at initial time, which is t=τ (simplest choice over many possible). Using this completely specified adjoint solution it can be shown that (Roustan and 1 Bocquet, 2005 ) Z Z ∗ µi = dtdx ci σ + dx c∗i c Ω ∂Ω0 Z Z + dtdS · c J ∗i − c∗i J − dtdS · c∗i cu . (6) ∂Ωb. ∂Ω+. 803. 6, 795–838, 2006. Inverse modelling for mercury over Europe Y. Roustan and M. Bocquet. Title Page Abstract. Introduction. Conclusions. References. Tables. Figures. J. I. J. I. Back. Close. Full Screen / Esc. Print Version Interactive Discussion. EGU.

(11) Let us denote n the unit vector orthogonal to the boundary, oriented outward (dS=dS n). In P OLAIR 3D, J · n stands actually for v dep c|b −E . That is why the choice ∗ dep ∗ J i · n=v ci |b allows for a simplification in the kernel: Z Z dtdS · c J ∗i − c∗i J → − dtdS · c∗i E , (7) ∂Ωb. 5. 10. ∂Ωb. with E=−E n. Therefore this specific choice of the adjoint solution makes the connection between the output and the surface emission clearer. In particular, this choice of adjoint solution stipulates dry deposition is to be taken into account in the calculation of the retroplume. Equations (6) and (7) make clear links between,. Inverse modelling for mercury over Europe Y. Roustan and M. Bocquet. Title Page Abstract. Introduction. • the volume emission σ,. Conclusions. References. Tables. Figures. J. I. J. I. Back. Close. • the boundary concentrations c on ∂Ω+ , and the output, the modelised observation µi . This decomposition explains a posteriori ∗ why the abstract function ci was introduced. 3.2. Application to a numerical transport model To perform numerical investigation, the domain Ω is discretised into a grid (seen S as a set of cells) Ω= k Ωk , where Ωk is a grid-cell. k indexes the mesh, with k=1, · · · , Nx Ny Nz Nt . A border cell belongs to one of the grid boundaries ∂Ω0 , ∂Ωτ , 20. 6, 795–838, 2006. • the surface emission E,. • the initial concentrations c on ∂Ω0 ,. 15. ACPD. Full Screen / Esc. Print Version Interactive Discussion. ∂Ωb , ∂Ωt , ∂Ωn , ∂Ωs , ∂Ωw , and ∂Ωe . Boundaries ∂Ω± are the grid-cells forming the one-layer boundaries of Ω.. EGU 804.

(12) 5. 10. 15. 20. In this paper, we apply our methods using the Chemistry Transport Model P OLAIR 3D (see Sportisse et al., 2002; Sartelet et al., 2002; Boutahar et al., 2004). The two chemistry modules implemented here are presented in Roustan et al. (2005). The numerical code is based on a first order time splitting algorithm allowing to separate temporally chemistry (when relevant), advection and diffusion. The advection scheme is a third-order Direct Space Time (DST) scheme (Spee, 1998) with the Koren-Sweby flux limiter function. Its related temporal scheme is explicit. The diffusion scheme is a spatially centred three point scheme (for each direction). Its related temporal scheme is a semi-implicit Rosenbrock scheme. The adjoint analysis can be carried out onto the numerical model. A scheme without approximation would require to compute the adjoint of the numerical model to obtain the adjoint numerical solutions. It is however easier to discretise the adjoint transport equation, which should be considered as a reasonable approximation in this context (Roustan and Bocquet, 20051 ). Detailed calculations show that the adjoint of P OLAIR 3D would be P OLAIR 3D itself, antisymmetric fields such as wind fields being reversed, if not for occasional non-linearity and if not the Kz time-dependence (M. Bocquet, unpublished). The error entailed by this approximation has been estimated. The result will given in the more intricate case of a complex chemistry model (Sect. 5). The results of the adjoint analysis sum up to the formula: X X µi = c∗i,k σk + c∗i ,k ck k∈Ω. k∈∂Ω0. X X + c∗i ,k Jk − ck Ji∗,k + c∗i ,k Fk , k∈∂Ωb. (8). ACPD 6, 795–838, 2006. Inverse modelling for mercury over Europe Y. Roustan and M. Bocquet. Title Page Abstract. Introduction. Conclusions. References. Tables. Figures. J. I. J. I. Back. Close. Full Screen / Esc. k∈∂Ω+ Print Version. 25. very similar to its continuous counterpart. Space and time volume elements which appear in the discretised sums have been integrated into the sources σk , space volume elements have been integrated into the initial concentrations ck |0 , whereas surface el∗ ∗ ements have been integrated into the emissions Ji ,k =−n · F i ,k and Jk =−n · J k , and 805. Interactive Discussion. EGU.

(13) 5. the advected fluxes Fk =−n · F k . Therefore, they all are expressed in units of mass. The numerical advected flux Fk could be specified precisely in terms of boundary concentrations and wind fields, with the details of the adjoint calculations. It is positive by definition on ∂Ω+ . In the case where J ∗i · n=v dep c∗i |b , Eq. (8) simplifies to X X µi = c∗i,k σk + c∗i ,k ck k∈Ω. +. X k∈∂Ωb. k∈∂Ω0. c∗i ,k Ek +. X. c∗i,k Fk .. 15. 20. 6, 795–838, 2006. Inverse modelling for mercury over Europe Y. Roustan and M. Bocquet. (9). k∈∂Ω+. This equation clearly establishes the connexion between modelised observation µi , and the forcing fields. We will use it extensively in the following.. 10. ACPD. 4. Towards inverse modelling of mercury The adjoint techniques which have been introduced in Sect. 3 are necessary technical tools for inverse modelling studies in a systematic approach. They allow to establish the cornerstone relations between data and forcing conditions to be inverted: Eq. (9). Inverse modelling of mercury can serve two purposes. The first one is the inversion of sources or emissions in order to improve inventories of emissions and sinks and more generally the budget of mercury. However, this might be beyond the scope of this paper, as will be seen. The second one consists in improving boundary conditions enforced and which, as observed, is crucial for the quality of the modelling in a regional domain. This is the main purpose of this work. 4.1. Improving annual mean boundary conditions Let us see how to proceed on an example of interest. 806. Title Page Abstract. Introduction. Conclusions. References. Tables. Figures. J. I. J. I. Back. Close. Full Screen / Esc. Print Version Interactive Discussion. EGU.

(14) 4.1.1.. 5. 10. 15. The monthly averaged (therefore possibly annual) measurements of elemental mercury for the four following Nordic EMEP stations are available: Mace Head (IE31 in the ¨ EMEP nomenclature), Pallas (FI96), Lista (NO99), and Rorvik (SE02). As suggested, and referring to our air limited domain, those stations are very much influenced by the West, East, or North incoming fluxes, and little by European sources. This can be checked on Table 2. We could assume uniform boundary conditions on the West, East and North faces of the domain as was done so far. Alternatively one can use non-uniform climatologies for the boundary conditions, such as those we were provided with by the EMEP MSC-E team for year 2001 and then 2002. The related fields will be called cW , cN , and cE . On Fig. 4 are given the monthly averaged concentrations of elemental mercury for the four sites obtained through observation, as well as direct simulations using EMEP uniform boundary conditions for year 2001, EMEP climatic boundary conditions for year 2001, and EMEP climatic boundary conditions for year 2002. It is then obvious on the graphs that it is much better to use the 2002 EMEP boundary conditions because of a better overall bias. 4.1.2.. 20. 25. The boundary conditions problem. The need for a background term. Because the inverse problem related to boundary conditions is ill-conditioned, it is important to use a background term which would penalise any too strong departure from the background. A typical background information would be given by first-guess climatologies, denoted bW , bN , and bE , and a background covariance matrix denoted B, describing a priori their typical fluctuations. Estimating the observation error covariance matrix R is realistic. However, estimating B is much more problematic. It is therefore wise to introduce a scalar parameter γ such that the background covariance matrix is actually γ −1 B. It will be estimated later on through a simple cross-validation approach.. ACPD 6, 795–838, 2006. Inverse modelling for mercury over Europe Y. Roustan and M. Bocquet. Title Page Abstract. Introduction. Conclusions. References. Tables. Figures. J. I. J. I. Back. Close. Full Screen / Esc. Print Version Interactive Discussion. EGU 807.

(15) 4.2. Inverting annual means boundary conditions. 5. ACPD. One improvement would be to allow for three degrees of freedom, so that the boundary conditions could be λW cW , λN cN , and λE cE , with λW , λN , λE , three scalars to be determined. The sensitivity of one of the measurement µi to the scalar λf is X δµi = c∗i ,k cfk uk , (10) δλf k∈∂Ω+ ∩∂Ωf. 10. where f stands for W, N or E. The set of measurements µi that we shall assimilate is the monthly averaged concentrations on the site Mace Head and on the site Pallas. Those correspond to p=24 measurements. Given these measurements, one would like to assess the values of the three boundary conditions. Define the 24×3 matrix [H]i ,f. 15. 20. δµi = , δλf. (11). where f is W, N or E. Let µ be the vector of the twenty-four observations, and let h be the vector whose component i is the (presumably known) contributions from all origin except incoming fluxes from West, East and North. Boundary conditions are stored in the vector λ: λ=(λW , λN , λE )T . Estimating them would imply minimising the discrepancy from the predicted concentrations to the observed ones. As mentioned earlier, it could also incorporate a background information, which tells one’s confidence in the climatological boundary conditions, on a priori grounds. A solution to this problem would therefore be the minimum of the cost function T γ 1 J = [µ − h − Hλ]T R−1 [µ − h − Hλ] + λ − λb B−1 λ − λb , (12) 2 2 where the first term of the right-hand side represents departure from the observations. The second term represents departure from the background. R is the observation error 808. 6, 795–838, 2006. Inverse modelling for mercury over Europe Y. Roustan and M. Bocquet. Title Page Abstract. Introduction. Conclusions. References. Tables. Figures. J. I. J. I. Back. Close. Full Screen / Esc. Print Version Interactive Discussion. EGU.

(16) 5. 10. covariance matrix. The observation error is generally considered to be less than 10% (Ryaboshapko et al., 2003). Therefore the value 0.1 ng.m−3 is chosen to represent it. 2 −6 The diagonal matrix R is then defined by [R]i j =δi j 0.01 (in ng m ). B is the background covariance matrix. λ is likely to be a three-vector of components W N N 1, if one trusts the climatology. The genuine physical first guesses are λW b b , λb b , and λEb bE , but background information can be “included” in B. We assume firstly that the error on the background term is not correlated from domain boundary to domain boundary. Secondly this error is assumed of the same order as the observation one (0.1 ng.m−3 ). We define the diagonal terms of the matrix B by:  −1 2  X skf bfk  , (13) [B]ff = 0.01 S . 20. 6, 795–838, 2006. Inverse modelling for mercury over Europe Y. Roustan and M. Bocquet. Title Page Abstract. Introduction. where f stands for W, N or E, sk and bk are the surface and the background information (climatology) for the cell k of the domain boundary f and S the total surface, P S= k∈∂Ω ∩(∪ ∂Ω ) skf . γ is the trade-off (between the two departures) parameter and is + f f dimensionless. Then, one obtains the normal equations h i−1 λ∗ = λb + γB−1 + HT R−1 H × HT R−1 (µ − h − Hλb ) . (14). Conclusions. References. Tables. Figures. J. I. J. I. After assimilation, the predicted values for the µi are given by µ∗ =Hλ∗ +h. The results are shown on Fig. 5 (diamonds). Because these graphs show the predicted values on the sites which provided with the assimilated measurements, it is not surprising that the improvement is great compared to the direct simulation. Nonetheless only three boundary variables were assimilated to obtain these results. More interestingly are the predicted elemental mercury concentrations on the sta¨ tions Lista and Rorvik, whose measurements were not used in the inversion. The results are shown on Fig. 6 (diamonds).. Back. Close. k∈∂Ω+ ∩∂Ωf f. 15. ACPD. f. 809. Full Screen / Esc. Print Version Interactive Discussion. EGU.

(17) 5. 10. The modelled concentrations are much closer to the observations than the simulation results without assimilation. Hence the assimilation of observations on the first two sites has yielded benefits on the last two. The assimilated parameters are reported in Table 3. It is however difficult to decide whether this improvement should be ascribed to the correction of a global bias only, or not. Fractional bias and fractional gross error (see Appendix) have been used as statistical indicators to evaluate the assimilation improvement with respect to the observed concentrations. The results are reported in Table 4. ¨ In particular, they concur with the improvements observed at Lista and Rorvik.. ACPD 6, 795–838, 2006. Inverse modelling for mercury over Europe Y. Roustan and M. Bocquet. 4.3. Improving the monthly averaged boundary conditions Title Page. 15. 20. 25. It is noteworthy that several measurements on Pallas are not shadowed properly by the assimilated values. This is particularly striking for the summer season. This may stem from the mercury arctic depletion events (MDE). The modelling of this phenomenon is currently addressed in several works (see Ariya et al., 2004; Calvert and Lindberg, 2003). How to pragmatically represent the phenomenon within a hemispherical mercury model can be found in Christensen et al. (2004) or Travnikov and Ryaboshapko (2002). However, the area-limited domain used here does not encompass the Arctic. A way out of this problem is to invert monthly averaged boundary conditions for the site Pallas which seems very sensitive to the phenomena. This will introduce intra-annual variability. Taking into account monthly averaged concentrations implies using several adjoint solutions, each of them with a sampling function πi describing an emitter lasting one month. Again climatologies for the year 2002 will be used. Because the spin-up is of about two weeks, the inversion of parameters tagging last months of 2001 will not be affected by the initial condition. However, January or February parameters might. That is why the inversion is implemented as a two year experiment. The adjoint solution are therefore calculated over two years. This lessens the impact of the initial condition. For the first year, the meteorological fields of 2001 are also used. The number of param810. Abstract. Introduction. Conclusions. References. Tables. Figures. J. I. J. I. Back. Close. Full Screen / Esc. Print Version Interactive Discussion. EGU.

(18) eters to invert is 14. Two are related to the West and East boundary conditions: λW and λE . Twelvenothers o are used to parameterise month after month the North boundary i. condition λN = λN 5. 10. 15. 20. i =1,···,12. . If one assumes those twelve values are uncorrelated, the. inverse problem would then almost certainly be very ill-conditioned as a not too important change in a month boundary conditions can surely be compensated by other changes in the eleven other parameters. It is therefore necessary to correlate them with a correlation length that we have chosen to be three months: h i |i −j | N N N − λ λ − λ = e− L , (15) [B]i j = E λN i b j b with L'3. The results of the inversion is reported in Fig. 5 for the sites which provided with the measurements used in the assimilation (circles). The results for the two other sites are reported in Fig. 6. The improvement is spectacular only on the Pallas station. It is barely improved elsewhere. In particular, the discrepancy observed in summertime ¨ at Rorvik are not accounted for. It is likely that only the Pallas station is significantly sensitive to the mercury depletion event (it has the greatest latitude). If we look at the whole domain the use of the monthly means has strong influence only on its northern part. The Fig. 7 shows the fractional bias between annual mean modelised concentrations computed with 3 and 14 inverted variables. The values of the 14 parameters of the inversion are given in Table 3. On Table 5 are reported the yearly averaged concentrations at the four Nordic stations, observed, simulated, and simulated using assimilation techniques on the Mace Head and Pallas sites. 4.4. Simple validation for γ. ACPD 6, 795–838, 2006. Inverse modelling for mercury over Europe Y. Roustan and M. Bocquet. Title Page Abstract. Introduction. Conclusions. References. Tables. Figures. J. I. J. I. Back. Close. Full Screen / Esc. Print Version Interactive Discussion. 25. So far, the measurements at Mace Head and Pallas were used to invert the boundary conditions parameters. However, an ad-hoc parameter γ was used to control the relative contributions of variances of observations and background to the inversion. 811. EGU.

(19) 5. 10. 15. 20. 25. The inversion can be repeated for several values of γ. The performance (r.m.s.) of the predicted concentrations using these inversions can then be assessed at Lista and ¨ Rorvik, the other two EMEP gaseous elemental mercury monitoring stations. If γ is very large, then the solution is forced by the background, the data do not tell more than the prior information and a strong mismatch is expected between the observed ¨ and predicted concentrations at Lista and Rorvik. On the other hand, if γ is small, the inversion only aims at giving an account of the observed concentrations at Mace Head and Pallas, even accounting for unrealistic errors. Those errors propagate by forecast ¨ to the other two stations. The forecast on Lista and Rorvik is therefore expected to be affected in this limit. As a consequence, there may be an optimal value of γ in between those two limits. The result of this test is represented on Fig. 8. There is an optimal value of about γ'6. All previous inversion were performed with γ=4 and we conclude that this guess was a good one, since the differences between forecasts with γ=4 and γ=6 are small.. ACPD 6, 795–838, 2006. Inverse modelling for mercury over Europe Y. Roustan and M. Bocquet. Title Page Abstract. Introduction. Conclusions. References. Tables. Figures. J. I. J. I. Back. Close. 4.5. Improving emissions inventory It has been demonstrated that it is possible to improve significantly predicted values of mercury dispersion in an area limited model by using inverse modelling on the boundary conditions. It should be possible to use a similar approach working on the emissions (natural or anthropogenic). The tests we have performed are negative in this respect. The related inverse problem is much too ill-conditioned (testified by the weak singular values of H), when using data from the four Nordic EMEP stations. This can be understood by the too weak sensitivities of those stations to the European emissions. At the stations, the actual contributions of the emissions represent 8%, 5%, 12% and 16% of the total gaseous mercury measured (to compare with, for instance, the Topolniky site (SK07) with a ratio of 40%). To improve emissions inventory using inverse modelling, one would therefore need stations where the emissions influence is significant (central European locations). Unfortunately, to our knowledge, no measurement of gaseous mercury is available on a 812. Full Screen / Esc. Print Version Interactive Discussion. EGU.

(20) 5. regular basis, except for the measurements performed at the stations already introduced, but where the emissions influence is too weak. We believe having such data on mercury would greatly help modellers. Moreover it is not so much GEM modelling itself which is at stake, but the improvement of models which ultimately predict deposition of oxidised forms of mercury. 5. Extension to a complex chemical model. 10. 15. 20. 25. So far, the inverse modelling approach presented here was based on a mercury dispersion model relying on the Petersen scheme. So that oxidised species were not properly modelled. In a first approximation, this was however acceptable since the boundary conditions to be inverted were concerned with the barely reactive gaseous elemental mercury. Nevertheless it is possible to extend this inverse modelling approach to cope with a more complex mercury chemistry. It is expected that this would be more relevant to measurement stations in the vicinity of anthropogenic sources. Out of the four EMEP ¨ stations considered here, this could be relevant to Rorvick as it is sensitive to northern European pollution. It was shown in Roustan and Bocquet (2005)1 that the adjoint analysis (needed for the inverse approach) can be extended to cope with oxidised species and their chemistry. Here, we rely on a seven aggregate species model developed in Roustan et al. (2005) in both gaseous and aqueous phases. Those considered in the gaseous phase are Hg(0), HgO, Hg(OH)2 and HgCl2 and their sum will be noted as total gaseous mercury (TGM) in the following. From the modellers perspective, this chemistry is linear in the mercury species, although it involves other species such as SO2 , O3 , OH, etc, which are forced into the model. The chemistry and transport equation are extended to: ∂c + div (uc) − div (K∇c) + Λ c + M c = σ . ∂t 813. ACPD 6, 795–838, 2006. Inverse modelling for mercury over Europe Y. Roustan and M. Bocquet. Title Page Abstract. Introduction. Conclusions. References. Tables. Figures. J. I. J. I. Back. Close. Full Screen / Esc. Print Version Interactive Discussion. (16). EGU.

(21) 5. c is the vector of mercury species (seven components in the model mentioned above). Λ is the diagonal matrix of the scavenging coefficient (species-dependent). M is the kinetic matrix describing the first-order (in mercury) chemistry and depends on forced fields of other species concentration. To generalise the adjoint analysis performed with the Petersen model, it is convenient T to introduce the canonical scalar product in the space of mercury species: hx, yi=x y. The measurement equation is now: Z µi = dtdx hπi (x, t), c(x, t)i . (17) Ω. 10. 15. 20. The sampling function πi is a vector in the space of species, and describes how each of the species is sampled. Even if the focus is on GEM in this work, πi will have four non-zero components since genuine measurements concern TGM. If we were able to distinguish the GEM component of the measurement we could work with a sampling function having only one non-zero component. The retro-transport equation generalises to: ∂c∗i. uc∗i. K∇c∗i. Λc∗i. . T. 6, 795–838, 2006. Inverse modelling for mercury over Europe Y. Roustan and M. Bocquet. Title Page Abstract. Introduction. Conclusions. References. Tables. Figures. J. I. J. I. Back. Close. c∗i. − div − div + +M = πi . (18) ∂t For a concentration measurement such as the one described by Eq. (17), the adjoint analysis is similar and one obtains Z Z ∗ µi = dtdx hci , σ i + dx hc∗i , ci Ω ∂Ω0 Z + dtdS · hc, J ∗i i − hc∗i , Ji ∂Ω Z b − dtdS · hc∗i , ciu . (19) −. . ACPD. ∂Ω+. It has been checked that the non-linearities introduced by the improved chemical scheme (some threshold being used to treat the aqueous phase) result in a very weak 814. Full Screen / Esc. Print Version Interactive Discussion. EGU.

(22) 5. violation of the additivity principle. As in the case of the Petersen scheme (Roustan 1 and Bocquet, 2005 ), the difference between a single multiple-component run and the sum of single-component runs, for each gaseous species, does not exceed 0.1%. Moreover, the error committed between the direct and the indirect calculations of the contributions to the mercury gaseous modelled concentration at Mace Head (IE31) and Pallas (FI96) has been estimated. The results are presented in Table 6. The approximations made in the computation of the adjoint solution and when taking the numerical model to be linear seem fairly contained.. ACPD 6, 795–838, 2006. Inverse modelling for mercury over Europe Y. Roustan and M. Bocquet. 5.1. Improving GEM boundary conditions using a complex chemical scheme 10. 15. 20. 25. We assume that at the boundary, far from anthropogenic sources, the fraction of oxidised species is low. It is set to zero. The parameters λ are therefore only scaling the concentration of GEM at the boundaries. One is therefore interested in the sensitivity of the TGM measurement to the gaseous incoming elemental mercury through one of the borders: X δµi = [c∗i ,(TGM,GEM) ] cfk uk , (20) k δλf k∈∂Ω+ ∩∂Ωf. where [c∗i ,(TGM,GEM) ] is the GEM component of c∗i computed with a TGM sampling function and f stands for W, E or N. This defines the matrix H according to Sect. 4.2. And the same data assimilation procedure can be applied. The measurement equation µ=Hλ+h requires also a different definition for h, which takes into account prior emissions of oxidised species. Aside from these differences, the cost function remains formally the same. γ is chosen to be γ'4 again. It has been checked that γ is not far from an optimal value as it was the case in the simple chemistry inversion problem. The results are reported in Fig. 9. The inverted parameters are given in Table 7. The statistics of those results are reported in Table 8. There are clear improvements ¨ due to the improved chemical model. This was expected for the Rorvick station. It has 815. Title Page Abstract. Introduction. Conclusions. References. Tables. Figures. J. I. J. I. Back. Close. Full Screen / Esc. Print Version Interactive Discussion. EGU.

(23) 5. 10. been emphasised that the northern European emissions have some influence on this station, so that the chemical reactions play a significant role in the mercury dispersion. ¨ The assimilated results are better for Pallas (FI96) and Rorvik (SE02), but they are slightly degraded for Mace Head (IE31) and Lista (NO99). Nevertheless this result is not really surprising. The modelled concentrations estimated with the climatic boundary conditions are only slightly overestimated at Mace Head and largely at Pallas. The assimilation process leads to decrease boundary conditions both in North and West (see Table 7). The contributions to the modelled concentrations are of the same order at Pallas, 0.44 ng.m−3 for the western boundary and 0.57 ng.m−3 for the northern one.. ACPD 6, 795–838, 2006. Inverse modelling for mercury over Europe Y. Roustan and M. Bocquet. 5.2. Possible improvement of the other inputs Title Page. 15. 20. 25. We have assumed until now that boundary conditions of oxidised species were negligible. This assumption is not too crude if we are interested in gaseous concentrations. It is less satisfactory regarding deposition fluxes. Direct assimilation of measured concentrations of TGM in order to improve the boundary conditions of oxidised species cannot be achieved with the available data. TGM concentrations are too poorly sensitive to the model parameters to invert (the inverse problem on the oxidised species only would be too ill-conditioned). At this point measurements of oxidised species could be useful, all the more since advances have been made in reactive gaseous and particulate mercury sampling (Landis et al., 2002). Another way to improve boundary conditions of oxidised species would consist in using deposition measurement data. Since deposition fluxes are much more sensitive to reactive gaseous mercury (RGM) concentrations (Roustan and Bocquet, 20051 ) the inverse problem could be better conditioned. This is however beyond the scope of this work. Nevertheless, it has been shown that the emission speciation was the key parameter for determining the mercury deposition fluxes in source areas (Pai et al., 1999). A similar problem is faced: more sampling stations with a central European location are needed. We believe that regular measurements of TGM and RGM could be used to 816. Abstract. Introduction. Conclusions. References. Tables. Figures. J. I. J. I. Back. Close. Full Screen / Esc. Print Version Interactive Discussion. EGU.

(24) improve efficiently the mercury emission inventory.. ACPD 6, 795–838, 2006. 6. Conclusions. 5. 10. 15. 20. 25. In this paper, we have attempted to correct some of the flaws inherent to regional modelling of mercury dispersion. Although using a regional model allows for a fine resolution description, it is very sensitive to external forcing fields, mainly boundary conditions (incoming mercury). To compensate for this weakness, we have assimilated observations of gaseous mercury to improve these boundary conditions, using the regional model P OLAIR 3D. It was shown to improve forecasts for gaseous mercury over Europe, not only on the monitoring stations which provided the assimilated data, but also on the others. We have resorted to the linearity of the dispersion and to the adjoint techniques to establish the linear relation between the concentrations at the monitoring stations and the forcing fields. The first tests were performed for annual boundary conditions. Yet, external influences, such as mercury depletion event, were accounted for by using monthly boundary conditions. The improvement on the GEM concentrations forecast with the Petersen scheme model and using assimilated boundary conditions is significant. It was bound to be so for the two EMEP stations which provided with the assimilated data but this conclusion still holds for the two remaining stations. There is however no significant improvement on the two last stations (whose measurements were not assimilated), when using the complex scheme model, as compared to the complex model without assimilated boundary conditions. This might be ascribed to the absence of well known boundary conditions for the oxidised species. We have concluded that the mercury observation network is insufficient to take full benefit of the approach. In particular it does not allow to invert emissions with confidence. This lack of data may be compensated in a near future since this is part of the EMEP monitoring strategy for the next four years. 817. Inverse modelling for mercury over Europe Y. Roustan and M. Bocquet. Title Page Abstract. Introduction. Conclusions. References. Tables. Figures. J. I. J. I. Back. Close. Full Screen / Esc. Print Version Interactive Discussion. EGU.

(25) 5. 10. It was shown that the adjoint analysis could be performed on oxidised mercury, when using a realistic chemistry. Hence, there exists a linear relation between the modelled oxidised mercury concentrations and the forcing fields. In this work were performed first experiments of inversion using a realistic model, but only inverting gaseous elemental mercury. The advantage of it on the simple model approach turned out not to 1 be obvious. In Roustan and Bocquet (2005) , we have shown that the sensitivity analysis could be extended to measurements of deposited mercury, not only air content measurements. Inversions of measurements of deposited mercury are therefore, in principle, possible. It should be investigated in future works, since many more measurements involving deposited oxidised mercury are available from the EMEP monitoring stations.. ACPD 6, 795–838, 2006. Inverse modelling for mercury over Europe Y. Roustan and M. Bocquet. Title Page. Appendix Statistical indicators. 15. Here are defined the statistical indicators used in this work. Consider a set of concentration measurements µi =1,···,p , and a set of predicted values for those measurements ci =1,···,p . Define the means p. p. 1X µ= µi p. 1X c= ci . p. and. i =1. (A1). Introduction. Conclusions. References. Tables. Figures. J. I. J. I. Back. Close. i =1. Full Screen / Esc. The bias and the fractional bias (FB) are defined by µ − c and. Abstract. 2. µ−c µ+c. ,. (A2). Print Version Interactive Discussion. EGU 818.

(26) and the fractional gross error (FE) is

(27) p

(28) ci − µi

(29) 2 X

(30)

(31)

(32)

(33) c + µ

(34) . p i i. ACPD (A3). 6, 795–838, 2006. i =1. Inverse modelling for mercury over Europe. The normalised root mean square is v u p u 1 X (µi − ci )2 t , p µc. (A4). i =1. 5. and eventually the individually normalised root mean square is v u p u 1 X (µi − ci )2 t . p µi ci. Y. Roustan and M. Bocquet. Title Page. (A5). Abstract. Introduction. Conclusions. References. Tables. Figures. J. I. J. I. Back. Close. i =1. Acknowledgements. The authors wish to thank I. Ilyin and the MSC-E team for kindly providing results of the MSCE model. Y. Roustan acknowledges financial support from ADEME and EDF.. References 10. 15. 20. Ariya, P. A., Dastoor, A. P., Amyot, M., Schroeder, W. H., Barrie, L., Anlauf, K., Raofie, F., Ryzhkov, A., Davignon, D., Lalonde, J., and Steffen, A.: The Arctic: a sink for mercury, Tellus, 56B, 397–403, 2004. 810 Baer, M. and Nester, K.: Parameterization of trace gas dry deposition velocities for a regional mesoscale diffusion model, Ann. Geophys., 10, 912–923, 1992. 799 ´ D., Roustan, Y., and Sportisse, B.: Development and Boutahar, J., Lacour, S., Mallet, V., Quelo, validation of a fully modular platform for numerical modelling of air pollution: POLAIR, Int. J. Environ. Pollut., 22(1/2), 17–28, 2004. 805 Brook, J. R., Zhang, L., Di-Giovanni, F., and Padro, J.: Description and evaluation of a model of deposition velocities for routine estimates of air pollutant dry deposition over North America. Part I: model development, Atmos. Environ., 33, 5037–5051, 1999. 799. 819. Full Screen / Esc. Print Version Interactive Discussion. EGU.

(35) 5. 10. 15. 20. 25. 30. Bullock, O. R. and Brehme, K. A.: Atmospheric mercury simulation using the CMAQ model: formulation description and analysis of wet deposition results, Atmos. Environ., 36, 2135– 2146, 2002. 797 Calvert, J. G. and Lindberg, S. E.: A modeling study of the mechanism of the halogen-ozonemercury homogeneous reactions in the troposphere during the polar spring, Atmos. Environ., 37, 4467–4481, 2003. 810 Christensen, J. H., Brandt, J., Frohn, L. M., and Skov, H.: Modelling of mercury with the Danish Eulerian Hemispheric Model, Atmos. Chem. Phys., 4, 2251–2257, 2004, SRef-ID: 1680-7324/acp/2004-4-2251. 797, 810 Hicks, B. B. and Liss, P. S.: Transfer of SO2 and other reactive gases across the air-sea interface, Tellus, 28, 348–354, 1976. 799 Ilyin, I., Ryaboshapko A., and Travnikov, O.: Heavy metal contamination on European and Hemisperical scale, EMEP Status report 3/2002, 2002. 797 Ilyin, I., Travnikov, O., Aas, W., and Uggerud, H. T.: Heavy metals: transboundary pollution of the environment, EMEP Status report 2/2003, 2003. 800 Landis, M. S., Stevens, R. K., Schaedlich, F., and Prestbo, E. M.: Development and characterization of annular denuder methodology for the measurement of divalent inorganic reactive gaseous mercury in ambient air, Environ. Sci. Technol., 36, 3000–3009, 2002. 816 Lin, X. and Tao, Y.: A numerical modelling study on regional mercury budget for eastern North America, Atmos. Chem. Phys., 3, 535–548, 2003, SRef-ID: 1680-7324/acp/2003-3-535. 797 Lindqvist, O. and Rodhe, H.: Atmospheric mercury – a review, Tellus, 37B, 136–159, 1985. 796 Pai, P., Karamchandani, P., and Seigneur, C.: Sensitivity of simulated atmospheric mercury concentrations and depositions to model input parameters, J. Geophys. Res., 104, 13 855– 13 868, 1999. 816 Petersen, G, Iverfeldt, A., and Munthe, J.: Atmospheric mercury species over central and northern Europe. Model calculations and comparison with observations from the nordic air and precipitation network for 1987 and 1988, Atmos. Environ., 29, 47–67, 1995. 798, 830 Roustan, Y., Bocquet, M., Musson Genon, L., and Sportisse, B.: Modeling atmospheric mercury at European scale with the Chemistry Transport Model P OLAIR 3D, Proceedings of Gloream 2004, 2005. 799, 805, 813 Ryaboshapko, A., Ilyin, I., Gusev, A., and Afinogenova, O.: Mercury in the atmosphere of. 820. ACPD 6, 795–838, 2006. Inverse modelling for mercury over Europe Y. Roustan and M. Bocquet. Title Page Abstract. Introduction. Conclusions. References. Tables. Figures. J. I. J. I. Back. Close. Full Screen / Esc. Print Version Interactive Discussion. EGU.

(36) 5. 10. 15. 20. 25. 30. Europe: concentrations, deposition patterns, transboundary fluxes, EMEP/MSC-E Report 7/1998, 1998. 801 Ryaboshapko, A., Bullock, R., Ebinghaus, R., Ilyin, I., Lohman, K., Munthe, J., Petersen, G., Seigneur, C., and Wngberg, I.: Comparison of mercury chemistry models, Atmospheric Environment, 36, 3881–3898, 2002. 796, 798 Ryaboshapko, A., Artz, R., Bullock, R., Christensen, J., Cohen, M., Dastoor, A., Davignon, D., Draxler, R., Ebinghaus, R., Ilyin, I., Munthe, J., Petersen, G., and Syrakov, D.: Intercomparison study of numerical models for long-range atmospheric transport of mercury. Stage II. Comparison of modeling results with observations obtained during short-term measuring campaigns, MSC-E Technical Report 1/2003, 2003. 809 ´ Sartelet, K., Boutahar, J., Quelo, D., Coll, I., Plion, P., and Sportisse, B: Development and Validation of a 3D Chemistry-Transport Model, POLAIR3D, by Comparison with Data from ESQUIF Campaign, Proceedings of the 6th Gloream workshop: Global and regional atmospheric modeling, 140–146, 2002. 805 Seigneur, C., Karamchandani, P., Lohman, K., Vijayaraghavan, K., and Shia, R.L.: Multiscale modeling of the atmospheric fate and transport of mercury, J. Geophys. Res., 106, 27 795– 27 809, 2001. 797 Seigneur, C., Karamchandani, P., Vijayaraghavan, K., Lohman, K., Shia, R., and Levin, L.: On the effect of spatial resolution on atmospheric mercury modeling, The Science of the Total Environment, 304, 73–81, 2003. 796 Spee, E.: Numerical methods in global transport models, PhD Thesis, Univ. Amsterdam, 1998. 805 ´ D., and Sartelet, K.: Some tracks in Air Pollution Sportisse, B., Boutahar, J., Debry, E., Quelo, Modeling. POLAIR: a numerical platform for air pollution modeling, RACSAM Journal of the Spanish Science Academy, Real Academia de Ciencias de Espana, 96, 507–528, 2002. 805 Travnikov, O. and Ryaboshapko, A.: Modelling of mercury hemispheric transport and depositions, MSC-E Tech. Report 6/2002, 2002. 810 Wesely, M. L. and Hicks, B. B.: A review of the current status of knowledge on dry deposition, Atmos. Environ., 34, 2261–2281, 2000. 799. ACPD 6, 795–838, 2006. Inverse modelling for mercury over Europe Y. Roustan and M. Bocquet. Title Page Abstract. Introduction. Conclusions. References. Tables. Figures. J. I. J. I. Back. Close. Full Screen / Esc. Print Version Interactive Discussion. EGU 821.

(37) ACPD 6, 795–838, 2006 Table 1. Elemental mercury mass budget over Europe for year 2001, using the Petersen’s chemistry. Mass figures are truncated to their first decimal. The last line lays the final mass budget equation. masses (in tons) initial mass (Mi ) ∂Ω0 final mass (Mf ) ∂Ωτ west flux ∂Ωw east flux ∂Ωe south flux ∂Ωs north flux ∂Ωn top flux ∂Ωt surface emission ∂Ωb anthropogenic natural reemission volume emission Ω anthropogenic natural reemission dry deposition ∂Ωb wet deposition ∂Ωb. incoming. 7713 1222 2411 1324 6328. outgoing. sum. 1752 6353 3794 1618 5722. 107 118 5961 −5131 −1383 −294 606. Inverse modelling for mercury over Europe Y. Roustan and M. Bocquet. Title Page Abstract. Introduction. Conclusions. References. 73 100 34. 73 100 34. Tables. Figures. J. I. 73. 73. J. I. Back. Close. 28 negligible. Mf −Mi −Σ flux. −28 negligible. Full Screen / Esc. 0.1. Print Version Interactive Discussion. EGU 822.

(38) ACPD 6, 795–838, 2006. Inverse modelling for mercury over Europe. Table 2. Contributions to the EMEP monitoring stations measurements of the West, East, North −3 and South incoming mercury, and the emissions of all kinds, in ng.m , as simulated with the simple scheme model. Station. West. East. North. South. Emiss.. Total. Mace Head (IE31) Pallas (FI96) Lista (NO99) ¨ Rorvik (SE02). 1.566. 0.049. 0.105. 0.008. 0.163. 1.900. 0.472. 0.514. 0.590. 0.005. 0.061. 1.697. 1.214. 0.148. 0.285. 0.022. 0.228. 1.950. 1.166. 0.203. 0.272. 0.024. 0.342. 2.066. Y. Roustan and M. Bocquet. Title Page Abstract. Introduction. Conclusions. References. Tables. Figures. J. I. J. I. Back. Close. Full Screen / Esc. Print Version Interactive Discussion. EGU 823.

(39) ACPD 6, 795–838, 2006. Inverse modelling for mercury over Europe Y. Roustan and M. Bocquet. Table 3. Assimilated coefficients for boundary conditions, simple model. # Par.. West. 3. 0.94. 14. 0.95. North Jan – 0.77 April – 0.85 July – 0.56 Oct – 0.52. 0.81 Feb – 0.82 May – 0.80 Aug – 0.33 Nov – 0.78. March – 0.92 June – 0.73 Sep – 0.24 Dec – 0.78. Title Page. East. Abstract. Introduction. 0.78. Conclusions. References. 0.84. Tables. Figures. J. I. J. I. Back. Close. Full Screen / Esc. Print Version Interactive Discussion. EGU 824.

(40) ACPD 6, 795–838, 2006. Inverse modelling for mercury over Europe. Table 4. Fractional Bias (FB) and Fractional Gross Error (FE) between observed concentrations and modelled ones using various boundary conditions (in %). Mace Head (IE31) FB FE uniform 2001 climatic 2001 3 variables – 2001 14 variables – 2001 climatic 2002 3 variables – 2002 14 variables – 2002. −12 −10 3 2 −3 4 3. 13 11 5 5 6 5 5. Pallas (FI96) FB FE −20 −25 −0.6 −0.3 −19 −3 −0.4. 20 25 9 2 20 8 2. Lista (NO99) FB FE. ¨ Rorvik (SE02) FB FE. −13 −14 2 2 −8 2 2. −21 −22 −8 −9 −17 −8 −9. 13 14 6 6 8 6 6. 21 22 10 10 17 10 10. Y. Roustan and M. Bocquet. Title Page Abstract. Introduction. Conclusions. References. Tables. Figures. J. I. J. I. Back. Close. Full Screen / Esc. Print Version Interactive Discussion. EGU 825.

(41) ACPD 6, 795–838, 2006. Inverse modelling for mercury over Europe Y. Roustan and M. Bocquet Table 5. Annual average concentration (in ng.m−3 ).. observation uniform 2001 climatic 2001 3 variables – 2001 14 variables – 2001 climatic 2002 3 variables – 2002 14 variables – 2002. Mace Head (IE31) 1.64. Pallas (FI96) 1.32. Lista (NO99) 1.65. ¨ Rorvik (SE02) 1.66. 1.86 1.82 1.60 1.61 1.71 1.59 1.61. 1.63 1.71 1.34 1.34 1.62 1.37 1.34. 1.90 1.91 1.65 1.65 1.80 1.64 1.65. 2.05 2.07 1.80 1.81 1.96 1.80 1.81. Title Page Abstract. Introduction. Conclusions. References. Tables. Figures. J. I. J. I. Back. Close. Full Screen / Esc. Print Version Interactive Discussion. EGU 826.

(42) ACPD 6, 795–838, 2006. Inverse modelling for mercury over Europe Y. Roustan and M. Bocquet. Table 6. Contribution to gaseous mercury concentrations in ng.m−3 for year 2001 over Europe, as computed from direct simulations (right), and from adjoint simulations (left).. Title Page Abstract. Introduction. Station. Winds. Emissions. Total. Conclusions. References. Mace Head (IE31) Pallas (FI96). 1.715–1.709. 0.119–0.098. 1.834–1.807. Tables. Figures. 1.527–1.524. 0.065–0.066. 1.592–1.588. J. I. J. I. Back. Close. Full Screen / Esc. Print Version Interactive Discussion. EGU 827.

(43) ACPD 6, 795–838, 2006. Inverse modelling for mercury over Europe Y. Roustan and M. Bocquet. Table 7. Assimilated coefficient for boundary conditions, complex model. # Par.. West. 3. 0.97. 14. 0.98. North Jan – 0.90 April – 0.90 July – 0.65 Oct – 0.57. 0.85 Feb – 0.91 May – 0.82 Aug – 0.47 Nov – 0.81. March – 0.93 June – 0.78 Sep – 0.41 Dec – 0.70. Title Page. East. Abstract. Introduction. 0.83. Conclusions. References. 0.88. Tables. Figures. J. I. J. I. Back. Close. Full Screen / Esc. Print Version Interactive Discussion. EGU 828.

(44) ACPD 6, 795–838, 2006. Inverse modelling for mercury over Europe Y. Roustan and M. Bocquet Table 8. Fractional Bias (FB) and Fractional Gross Error (FE) between observed concentrations and modelled ones using various boundary conditions with the complex chemistry model (in %). Mace Head (IE31) FB FE climatic 2002 3 variables – 2002 14 variables – 2002. −0.6 3 3. 5 5 4. Pallas (FI96) FB FE −17 18 −5 8 −3 4. Lista (NO99) FB FE. ¨ Rorvik (SE02) FB FE. −3 4 5. −8 −2 −2. 5 7 7. 9 8 7. Title Page Abstract. Introduction. Conclusions. References. Tables. Figures. J. I. J. I. Back. Close. Full Screen / Esc. Print Version Interactive Discussion. EGU 829.

(45) ACPD 6, 795–838, 2006. Inverse modelling for mercury over Europe Y. Roustan and M. Bocquet. Title Page. Fig. 1. Schematic of the Petersen et al. (1995) mercury chemistry model.. Abstract. Introduction. Conclusions. References. Tables. Figures. J. I. J. I. Back. Close. Full Screen / Esc. Print Version Interactive Discussion. EGU 830.

(46) ACPD 6, 795–838, 2006. Inverse modelling for mercury over Europe. 70°N. 500. FI96 65°N. 200 100. 60°N. NO99. Abstract. Introduction. Conclusions. References. Tables. Figures. 2. J. I. 1. J. I. Back. Close. 20 IE31. 10. SK07. 5 45°N. 40°N. 10°W. 5°W. 0°. 5°E. 10°E. 15°E. Title Page. 50. SE02. 55°N. 50°N. Y. Roustan and M. Bocquet. 20°E. 25°E. 30°E. 35°E. Full Screen / Esc −2. −1. Fig. 2. Mean annual emissions (in µg m yr ) over the domain D . Symbols N and • indicate EMEP gaseous mercury monitoring stations and Topolniky station, respectively.. Print Version Interactive Discussion. EGU 831.

(47) ACPD 6, 795–838, 2006. 4. Y. Roustan and M. Bocquet: Inverse Inverse modelling for mercury over Europe. 1. The justification for intro Y. Roustan and characterise c∗i complete M. Bocquet must be specified. As is clearly Title Pageseen from responds to a Introduction transport Abstract is theConclusions oppositeReferences of the di quence, an outgoing (fro Tables Figures direct model is actually a I speci model. JIn order to we therefore needI to spe J time. For simplicity, Close Back. 0,5. 0 -3. -3. -3. -3. Correl. 0 ng.m / 1.5 ng.m. -0,5. Correl. 5 ng.m / 1.5 ng.m -3. Correl. 5 ng.m / 0 ng.m. -3. -1 1 week. 2 week. 3 week. ∀ (x, t) ∈. Full Screen / Esc. Fig. 3. Influence of initial conditions: spatial correlation between simulation results with different −3 Fig. Influence of−3initial conditions : spatial correlation initial bulk3. conditions, 0 ng.m , 1.5 ng.m (the reference case) and 5 ng.m−3 . between −3. simulation results with different initial bulk conditions, 0 ng.m 1.5 ng.m−3 (the reference case) and 5 ng.m−3 . 832. ,. fluxes is close to the ground one can expect to find a rela-. Print Version. is assumed (among othe Interactive Discussion In addition, the diffu the boundary EGU∂D are su pared to the advected fl 0. However at the surfa.

(48) Lista (NO99) Rörvik (SE02). 1.214. 0.148. 0.285. 0.022. 0.228. 1.950. 1.166. 0.203. 0.272. 0.024. 0.342. 2.066. ACPD [H]i,f = 6, 795–838, 2006. IE31 - Mace Head. FI96 - Pallas. 2.5. 2.5. 2. 2. 1.5. 1. matrix. 1.5. J F M A M J J A S O N D. Observation Polair3D uniform BC 2001. J F M A M J J A S O N D. 1. Polair3D climatic BC 2001 Polair3D climatic BC 2002. NO99 - Lista. SE02 - Rorvik. 2.5. 2.5. 2. where f is W, N or E. Let µ be t four observations, let h be Inverseand modelling forthe i is the (presumably contrib mercury known) over Europe cept incoming fluxes from West, Ea Y. Roustan and conditions are stored in the vector λ M. Bocquet Estimating them would imply min from the predicted concentrations t Page mentioned earlier, itTitlecould also inco Introduction Abstract formation, which tells one’s confide boundary conditions, onReferences a priori gr Conclusions problem would therefore be the mi Tables Figures tion. 2. J= 1.5. 1. 1.5. J F M A M J J A S O N D. J F M A M J J A S O N D. δµ δλ. 1. 1 I J T [µ − h − Hλ] R−1 [µ − 2 I J γ T −1 + [λ − Back λb ] B Close [λ − λb ] 2 Full Screen / Esc. where the first term of the right-han Fig. 4. Direct simulations results for different boundary conditions (year 2001). The EMEP Fig. 4. conditions Direct simulations results for different boundary conditions 2002 boundary should clearly be preferred even for a 2001 simulation as boundary ture from the observations. The se Print Version (year 2001). The EMEP 2002 boundary conditions should clearly climatology. be preferred even for a 2001 simulation as boundary climatology.. 4.1.2 The need for a background term. 833. parture from the background. R is Interactive Discussion variance matrix. The observation e ered to be less than 10% (Ryabosha EGU −3 fore the value 0.1 ng.m is chos diagonal matrix R is then defined 2. −6.

(49) After assimilation, the predicted values for the µi are given by µ∗ = Hλ∗ + h. The results are shown on Fig.5 (diamonds). Because these graphs show the predicted values on the sites which provided with the assimilated measurements, it is not surprising that the improvement is great compared to the direct simulation. Nonetheless only three boundary variables were assimilated to obtain these results. More interIE31 - Mace Head. FI96 - Pallas. 2.5. 2.5. 2. 2. 1.5. 1. 1.5. 1. Jul - 0.56 Oct - 0.52. ACPD. A N. 6, 795–838, 2006. Inverse modelling are reported in table 4. In for partic mercury over Europe provements observed at Lista a Y. Roustan and M. Bocquet. Table 4. Fractional Bias (FB) and a tween observed concentrations an Title Page boundary conditions (in %). Abstract. Introduction. Conclusions. References. Tables. Figures. Mace Hea (IE31) FB F I J -12 1 5. Those two graphs display the assimilated concentrations at Pallas.uniform 2001 Fig. Fig. 5. Those two graphs display the assimilated concentrations at Mace Head and I J The Mace first inversion with three parameters does not take into account intra-annual variability. climatic 2001 -10 1 Head and Pallas. The first inversion with three parameters The second inversion with fourteen parameters take into account the variability of the northern 3 variables -Back 2001 3 Close does not take into account intra-annual variability. The second inboundary conditions. The observed concentrations and the simulated ones are also given for 14 variables -Full 2001 2 version with fourteen parameters take into account the variability of comparison. Screen / Esc climatic 2002 -3 the northern boundary conditions. The observed concentrations and 3 variables - 2002 the simulated ones are also given for comparison. Print Version 4 14 variables - 2002 3 J F M A M J. J A S O N D. Observation Polair3D climatic 2002. J F M A M J J A S O N D. Polair3D 2002 - 3 variables Polair3D 2002 - 14 variables. Interactive Discussion. estingly are the predicted elemental mercury concentrations on the stations Lista and Rörvik, whose measurements were are shown on Fig.6 (dinot used in the inversion. The results 834 amonds). The modelled concentrations are much closer to. EGU. 4.3 Improving the monthly av a.

(50) the and the northern northern boundary conditions. The observed concentrations and the the simulated simulated ones are also given for comparison.. climatic 2002 2002 -3 climatic -3 variables -- 2002 2002 33 variables 44 ACPD 33 14 variables variables -- 2002 2002 14. estingly estingly are the predicted elemental mercury concentrations on on the the stations Lista and Rörvik, whose measurements were not not used in the inversion. The results are shown on Fig.6 (diamonds). amonds). The modelled concentrations are much closer to. 6, 795–838, 2006. NO99 NO99 - Lista. SE02 - Rorvik Rorvik. 4.3 4.3. Inverse modelling for mercury the over Europe av Improving the monthly monthly a Improving Y. Roustan and. is noteworthy noteworthy that several several me m ItIt is M. that Bocquet 2.5 2.5 2.5 2.5 shadowed properly properly by by the the assim assi shadowed 22 22 ularly the ularly striking striking for for the summer summer Title Page the the mercury mercury arctic arctic depletion depletion ee Introduction Abstract 1.5 1.5 1.5 1.5 of of this this phenomenon phenomenon isis currentl current Conclusions References (see (see Ariya Ariya et et al. al. (2004), (2004), Calver Calve 11 11 J F M A M J J J F M A M J JJ A J F M A M J J A S O N D A S N D D S O O N Tables represent Figures the to to pragmatically pragmatically represent the Polair3D 2002 - 3 variables Observation variables Observation Polair3D 2002 - 14 variables Polair3D climatic 2002 variables Polair3D spherical spherical mercury mercury model model can can bb I J (2004)) (2004)) or or (Travnikov (Travnikov and and Rya Ry Fig. 6. Those assimilated concentrations 6. twodisplay graphsthedisplay the concentrations at The first ¨ at Fig. Fig. 6. Those two graphs assimilated at Lista and Rorvik. I used J the domain the area-limited area-limited domain used inversion parameters doesinversion not take into account intra-annual variability. The second Listawith andthree Rörvik. The first with three parameters does not Lista and not inversion with fourteen parameters take into account the variability of the northern boundary Back out Arctic. this Arctic. A A way way out of ofClose this prob pro take into into account intra-annual variability. The second inversion with take with conditions. The observed concentrations and the simulated ones are also given for comparison. eraged conditions fo eraged boundary boundary conditions fo Full Screen / Esc fourteen parameters take into account the variability of the northern fourteen northern very very sensitive sensitive to to the the phenomen phenome boundary conditions. The observed concentrations and the simuboundary simuPrint Version annual lated ones ones are also given for comparison. annual variability. variability. lated Taking account monthly Interactive Discussion Taking into into account monthl the observations than the simulation results without assimplies the plies using using several several adjoint adjoint so s EGU ilation. Hence the assimilation of observations on the first aa sampling ilation. sampling function function ππii descr descr 835 two sites has yielded benefits on the last two. The assimimonth. two month. Again Again climatologies climatologies fo fo.